A family member has applied for the same position. They haven't heard anything either. No news is good news though, as you are likely to have passed an initial sift. I'm sure I saw someone on here who was rejected within ten minutes of applying! I think HR set up a computer to look for or reject certain things.
Even though it didn't involve Southern, as a qualified driver when I swapped companies, it wasn't a quick or smooth process! The company will be juggling with what training they need to provide, what classroom instructors they've got and how many courses they'll provide this year and who to put on each one, what Driver Instructors they've got.
Sometimes plans will change - where I work, one of the trainees was involved in a road accident so was off work for a few weeks. Something like this would not only set back that trainee, but the Driver Instructor they would've been with would now be with them for a few weeks longer to finish their training and wouldn't be available for the next trainee they should've had - there will be juggling around and perhaps someone gets told "we've put your application on hold," when they would otherwise have been given a start date.
Also, classroom instructors don't just train Trainee Drivers, there are also Qualified Drivers who will have different training needs - some might know 3rd rail already, some might not, some might have just done diesels before. Their training will have to be planned and more juggling around as to when to fit it in. Drivers who return from long term sick leave might need refresher training - where to fit them into the grand scheme of things?
It is frustrating waiting to hear back, but it is quite common on the railway to apply for a job and not hear back for a while, or even to have an interview, get a phonecall to tell you you've got the job followed by an email to tell you you're on hold! So don't go celebrating until you've got a start date in writing!